Study of three‐dimensional Rayleigh–Taylor instability in compressible fluids through level set method and parallel computation

An improved particle correction procedure for particle level set method is proposed and applied to the simulation of Rayleigh–Taylor instability (RTI) of the incompressible two-phase immiscible fluids. In the proposed method, an improved particle correction method is developed to deal with all the relative positions between escaped particles and cell corners, which can reduce the disturbance arising in the distance function correction process due to the non-normal direction movement of escaped particles. The improved method is validated through accurately capturing the moving interface of the Zalesak's disk. Furthermore, coupled with the projection method for solving the Navier–Stokes equations, the time-dependent evolution of the RTI interface over a wide range of Reynolds numbers, Atwood numbers and Weber numbers are numerically investigated. A good agreement between the present results and the existing analytical solutions is obtained and the accuracy of the proposed method is further verified. Moreover, the effects of control parameters including viscosity, density ratio, and surface tension coefficient on the evolution of RTI are analyzed in detail, and a critical Weber number for the development of RTI is found.

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Numerical Study for the Three-Dimensional Rayleigh–Taylor Instability through the TVD/AC Scheme and Parallel Computation

Journal of Computational Physics ◽

10.1006/jcph.1996.0142 ◽

1996 ◽

Vol 126 (2) ◽

pp. 343-355 ◽

Cited By ~ 39

Author(s):

X.L. Li ◽

B.X. Jin ◽

J. Glimm

Keyword(s):

Parallel Computation ◽

Numerical Study ◽

Three Dimensional ◽

Taylor Instability ◽

Rayleigh Taylor Instability

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Numerical and Experimental Analysis of the Growth of Gravitational Interfacial Instability Generated by Two Viscous Fluids of Different Densities

Journal of Fluids ◽

10.1155/2013/532016 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11

Author(s):

Snehamoy Majumder ◽

Debajit Saha ◽

Partha Mishra

Keyword(s):

Level Set Method ◽

Level Set ◽

Gravitational Instability ◽

Physical Phenomenon ◽

Taylor Instability ◽

Interfacial Instability ◽

Heaviside Function ◽

Two Fluids ◽

Gravity Driven ◽

Rayleigh Taylor Instability

In the geophysical context, there are a wide variety of mechanisms which may lead to the formation of unstable density stratification, leading in turn to the development of the Rayleigh-Taylor instability and, more generally, interfacial gravity-driven instabilities, which involves moving boundaries and interfaces. The purpose of this work is to study the level set method and to apply the process to study the Rayleigh-Taylor instability experimentally and numerically. With the help of a simple, inexpensive experimental arrangement, the R-T instability has been visualized with moderate accuracy for real fluids. The same physical phenomenon has been investigated numerically to track the interface of two fluids of different densities to observe the gravitational instability with the application of level set method coupled with volume of fraction replacing the Heaviside function. Good agreement between theory and experimental results was found and growth of instability for both of the methods has been plotted.

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